Subgroups — #11763887

Order 1088.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63254	C₂	1	1	yes	maximal, characteristic
2	C₂×#63247	C₂	1	4	yes	maximal, complemented
3	#10587678	C₂	1	8	yes	maximal, complemented
4	D₁₇⋊M₁₆	C₂	1	2	yes	maximal, complemented
5	C₂×D₄×C₁₇	C₄	1	1	yes	characteristic
6	C₂×C₂²⋊D₁₇	C₄	1	2	yes	—
7	C₂²×Dic₁₇	C₂²	1	2	yes	—
8	#63254	C₄	1	4	yes	—
9	#63254	C₂²	1	4	yes	—
10	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₄	C₄	1	1	yes	characteristic
12	#63247	C₂²	1	4	yes	—
13	#63247	C₂²	1	8	yes	complemented
14	C₂×#3624	C₂²	1	8	yes	complemented
15	#63243	C₂²	1	4	yes	complemented
16	#63242	C₂²	1	4	yes	complemented
17	C₂³×C₁₇	C₂×C₄	1	2	yes	—
18	C₂²×D₁₇	C₂×C₄	1	1	yes	characteristic
19	D₄×C₁₇	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂²⋊D₁₇	C₂×C₄	1	8	yes	—
22	C₂×Dic₁₇	C₂×C₄	1	2	yes	—
23	C₂×Dic₁₇	C₂×C₄	1	4	yes	—
24	C₂×Dic₁₇	C₂³	1	4	yes	—
25	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
26	C₄×D₁₇	C₂×C₄	1	2	yes	—
27	C₄×D₁₇	C₂³	1	2	yes	—
28	Dic₃₄	C₂×C₄	1	4	yes	—
29	#3624	C₂³	1	8	yes	—
30	C₂²×C₁₇	—	4	2	no	—
31	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₁₇	C₂²×C₄	1	4	yes	—
33	C₂×D₁₇	—	4	1	no	—
34	C₂×D₁₇	C₂²×C₄	1	2	yes	—
35	C₄×C₁₇	C₂²×C₄	1	2	yes	—
36	Dic₁₇	C₂²×C₄	1	4	yes	—
37	Dic₁₇	C₂²×C₄	1	1	yes	characteristic
38	Dic₁₇	C₂⁴	1	1	yes	characteristic
39	#568	—	17	1	no	maximal, Sylow
40	C₂×C₁₇	—	2	1	no	—
41	C₂×C₁₇	—	2	4	no	—
42	C₂×C₁₇	C₂³×C₄	1	1	yes	characteristic
43	D₁₇	—	2	2	no	—
44	C₂×#41	—	17	1	no	—
45	#131	—	17	8	no	—
46	C₂×M₁₆	—	17	2	no	—
47	C₂×M₁₆	—	17	4	no	—
48	C₁₇	#568	1	1	yes	characteristic, complemented, Sylow
49	#41	—	17	4	no	—
50	#41	—	17	4	no	—
51	C₂×Q₈	—	17	1	no	—
52	C₂×D₄	—	17	2	no	—
53	C₂×D₄	#595	1	1	yes	characteristic
54	C₂²×C₄	—	17	2	no	—
55	C₂²×C₄	—	17	1	no	—
56	M₁₆	—	17	4	no	—
57	M₁₆	—	17	4	no	—
58	M₁₆	—	17	8	no	—
59	C₂×C₈	—	17	4	no	—
60	C₂×C₈	—	17	8	no	—
61	C₂³	—	17	1	no	—
62	C₂³	C₂×#595	1	2	yes	—
63	Q₈	—	17	4	no	—
64	D₄	—	17	8	no	—
65	D₄	C₂×#595	1	4	yes	—
66	C₂×C₄	—	17	4	no	—
67	C₂×C₄	—	17	1	no	—
68	C₂×C₄	—	17	2	no	—
69	C₂×C₄	—	17	4	no	—
70	C₂×C₄	—	17	2	no	—
71	C₂×C₄	—	17	2	no	—
72	C₂×C₄	C₂×#595	1	1	yes	characteristic
73	C₈	—	17	8	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	17	2	no	—
76	C₂²	—	68	1	no	—
77	C₂²	C₂²×#595	1	1	yes	characteristic
78	C₂²	C₂²×#595	1	4	yes	—
79	C₄	—	17	1	no	—
80	C₄	—	17	1	no	—
81	C₄	—	17	4	no	—
82	C₄	C₂²×#595	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	2	4	no	—
85	C₂	—	34	2	no	—
86	C₂	C₂³×#595	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#595
commutator, socle	C₂×C₁₇	C₂³×C₄
Fitting	C₂×D₄×C₁₇	C₄
prime radical	C₂×#63254	C₂
cosocle	Dic₁₇	C₂⁴
hypercenter	C₂×D₄	#595
hypocenter	C₁₇	#568
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×D₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#63247	C₂	semidirect
3. #10587678	C₂	semidirect
4. D₁₇⋊M₁₆	C₂	semidirect
13. #63247	C₂²	semidirect
14. C₂×#3624	C₂²	semidirect
15. #63243	C₂²	semidirect
16. #63242	C₂²	semidirect
48. C₁₇	#568	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#63254	2
C₂×#63247	2
#10587678	2
D₁₇⋊M₁₆	2
#568	17